Nanoscopic wire-based devices and arrays

ABSTRACT

Electrical devices comprised of nanoscopic wires are described, along with methods of their manufacture and use. The nanoscopic wires can be nanotubes, preferably single-walled carbon nanotubes. They can be arranged in crossbar arrays using chemically patterned surfaces for direction, via chemical vapor deposition. Chemical vapor deposition also can be used to form nanotubes in arrays in the presence of directing electric fields, optionally in combination with self-assembled monolayer patterns. Bistable devices are described.

RELATED APPLICATIONS

This application is divisional of U.S. patent application Ser. No.10/973,665, filed Oct. 26, 2004, which is a divisional of U.S. patentapplication Ser. No. 10/812,653, filed Mar. 29, 2004, which is acontinuation of U.S. patent application Ser. No. 10/033,369, filed Oct.24, 2001, which is a continuation of International Patent ApplicationSerial No. PCT/US00/18138, filed Jun. 30, 2000, which claims priority toU.S. Provisional Patent Application Ser. No. 60/142,216, filed Jul. 2,1999.

GOVERNMENT SPONSORSHIP

This invention was sponsored by the Office of Naval Research/DefenseAdvanced Research Projects contract number N00014-99-0495. Thegovernment has certain rights in the invention.

FIELD OF THE INVENTION

The present invention relates generally to the controlled formationand/or orientation of large molecules, such as nanotubes, on surfaces,and more particularly to formation of carbon nanotubes on surfaces formaking nanoscopic-scale electronic devices such as memory arrays,configurable logic and other computer elements.

BACKGROUND OF THE INVENTION

During the past several decades there has been a nearly constantexponential growth in the capabilities of silicon-based microelectronicsleading, for example, to tremendous advances in our computationalcapabilities. Silicon-based microelectronics, however, can be made onlyso small. That is, there is a size limitation smaller than whichsilicon-based microelectronics cannot be fabricated. Specifically, theNational Technology Roadmap for Semiconductors (SEMATECH, Austin, 1997)suggest that silicon-based microelectronics, which are typically said tofollow “Moore's Law”, will continue only to about the year 2010. At thistime, two factors are expected to bring Moore's scaling to an end.First, fundamental physical limitations will be reached for both deviceelements and wire interconnects that will prevent current designs fromfunctioning reliably. Second, the concurrent exponential increase infabrication (FAB) facility cost is expected to make it uneconomical toconsider increasing integration levels further (using silicontechnology) even if it is physically meaningful.

These factors, and the expected benefits that could be derived fromfurther dramatic increases in computational power in the relatively nearfuture, have led many to consider new devices and computerarchitectures. In particular, there has been considerable interest indeveloping the concept of molecular electronics. Molecular-basedelectronics can in principle overcome the fundamental physical andeconomic limitations of silicon-based microelectronics; it is physicallypossible to have single molecular devices. For example, a conformationalchange that varies the conjugation in a molecule could behave as aswitch or rectifier.

Investigation has taken place into manipulation of molecules at surfacesfor electronic applications. Liu, et al, in “Controlled Deposition ofIndividual Single-Walled Carbon Nanotubes on Chemically FunctionalizedTemplates,” Chem. Phys. Lett. 303 (1999) 125-129 report procedures forproducing individual, short carbon nanotube segments and for theirdeposition on chemically functionalized nanolithographic templates.Specifically, a patterned self-assembled monolayer is formed on asurface and a carbon nanotube is adsorbed onto the surface in anorientation corresponding to the pattern. The authors also describeconnection of an individual carbon nanotube between two electrodes.

Monolayers have been used to provide molecular electronic devices.Collier et al. describes the use of a Langmuir-Blodgett film of rotaxanemolecules interposed between lithographically fabricated wires ofmicron-scale diameter (Science Vol. 285, p. 391, 1999). This system isuseful for read-only memory devices, however, as the configurableelements involve irreversible oxidation of the rotaxane.

Other studies report a single carbon nanotube constructed as anelectronic switch (Collins, et al., Science 278 (1997)100), and aroom-temperature transistor (Tans, et al., Nature 393 (1998) 49).

To date, there has been considerable progress in characterization of theelectrical behavior of individual or small numbers of molecule devices.However, a significant need exists for improvement in molecule-scaleelectronics, especially for integrating bistable and switchable devicesfor high-density memory arrays.

SUMMARY OF THE INVENTION

The present invention provides a series of nanoscopic-scale electronicelements, methods of making nanoscopic-scale electronic elements, andmethods of use of nanoscopic-scale electronic elements.

In one aspect, the invention provides a nanoscopic-scale electronicdevice. The device is defined by an electrical crossbar array thatincludes at least one nanoscopic wire. The crossbar array can be of avariety of configurations such as a 1×8 array, 8×8 array, etc. The arraycan include contact electrodes in electrical contact with various wires,for example, by covalent attachment. Crossbar arrays provided accordingto the invention have densities up to about 10¹²/cm².

In another aspect the invention provides techniques for makingnanoscopic-scale electronic devices. In one embodiment, the inventioninvolves forming a nanoscopic wire on a surface in a pattern dictated bya chemically patterned surface. The nanoscopic wire can be a pre-formedwire, in which case the method involves applying the pre-formed wire tothe surface in the pattern. Alternatively, the nanoscopic wire can begrown on the surface in the pattern. The chemically patterned surfacecan be patterned to direct assembly or growth of the nanoscopic wire ina predetermined orientation useful for a particular electronic device.

In another embodiment the invention provides a method involving growinga nanoscopic wire in the presence of an electric field. The field is ofintensity sufficient to orient the growth of the wire. This method can,optionally, be used in combination with a method involving growing ananoscopic wire on a self-assembled monolayer. In all methods,nanoscopic wire growth can be carried out via chemical vapor deposition(CVD).

In other embodiments, the invention provides a method involving forminga nanoscopic wire on a surface in a pattern dictated by a mechanicallypatterned surface or by gas flow.

In another aspect, the invention provides methods of using electronicdevices. In one aspect, a method of the invention involves providing acrossbar array comprising at least two wires in crossbar arrayorientation, where the wires are free of contact with each other, andbringing the wires into contact with each other. The wires are contactedat a crossbar array junction at which they are alternately brought intocontact with each other and released from contact with each other. Inone embodiment the wires are nanoscopic wires.

Another aspect of the present invention provides an article comprising aself-assembled monolayer defining a delineated pattern. At least twocrossed wires are associated with the self-assembled monolayer in whichat least one of the wires is a nanoscopic wire. In another aspect, theinvention provides an article comprising an electric crossbar arraycomprising at least two crossed wires defining a memory element able tobe switched between at least two readable states. The device is free ofauxiliary circuitry other than the at least two crossed wires definingthe memory element.

In another aspect, the present invention provides a method comprisingswitching a memory element of a crossbar array between “on” and “off”states by alternatively biasing, at similar and opposite polarity, wiresthat cross the array to define the element.

In another aspect, the present invention provides an article comprisingan electric crossbar array comprising at least two crossed nanoscopicwires defining a memory element capable of being switched reversiblybetween at least two readable states.

In another aspect, the present invention provides an article comprisingan electrical crossbar array comprising at least two crossed nanoscopicwires defining a memory element capable of being switched between atleast two readable states. The memory element is non-volatile.

In another aspect, the present invention provides an article comprisingan electrical crossbar array comprising at least two crossed wiresdefining a diode. The device is free of auxiliary circuitry other thanthe at least two crossed wires defining the diode.

In another aspect, the present invention provides a method comprisingproviding a mixture of metallic nanotubes in semiconducting nanotubes.The method also involves separating the metallic nanotubes from thesemiconducting nanotubes.

In all of the embodiments of the invention, preferred nanoscopic wiresare nanotubes.

Other advantages, novel features, and objects of the invention willbecome apparent from the following detailed description of the inventionwhen considered in conjunction with the accompanying drawings, which areschematic and which are not intended to be drawn to scale. In thefigures, each identical or nearly identical component that isillustrated in various figures is represented by a single numeral. Forpurposes of clarity, not every component is labeled in every figure, noris every component of each embodiment of the invention shown whereillustration is not necessary to allow those of ordinary skill in theart to understand the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates, schematically, techniques for preparing a patternedself-assembled monolayer on a surface, and use of the patternedmonolayer for growth of a nanoscopic wire;

FIG. 2 illustrates, schematically, use of patterned self-assembledmonolayers for formation of overlapping (intersecting) nanoscopic wires;

FIGS. 3A and 3B illustrate, schematically, catalytic growth of atwo-dimensional nanoscopic wire array;

FIG. 4 illustrates, schematically and graphically, a bistable nanoscopicwire junction (memory element) and switching mechanism in terms ofenergy;

FIG. 5 illustrates, schematically and graphically, a bistable/nanoscopicwire junction (memory element) and switching mechanism in terms ofenergy;

FIGS. 6A, 6B, and 6C illustrate, schematically, bistable nanoscopic wirecrossbar memory elements (crossbar junctions) in “on” and “off” statesincluding three arrangements for provision of separate oppositelycharged molecules;

FIG. 7 is a cut away schematic illustration of a crossbar array of theinvention.

FIG. 8 shows a schematic of a device of the invention featuring acrossbar array;

FIG. 9A shows a top view of a crossbar array, illustrating cross talk;

FIG. 9B shows a top view of a crossbar array having diode junctionsfeaturing intrinsic rectifying behavior;

FIG. 10A shows a schematic of an article having parallel trenches andcatalyst nanoparticles for the production of crossed wires;

FIG. 10B shows a device having a crossbar array of nanowires in paralleltrenches crossed by nanowires positioned over the trenches;

FIG. 11 shows plots of energy, ET for a single 20 nm device as afunction of separation at a junction;

FIG. 12 shows calculated structures of single wall nanotubes (SWNTs) inthe off and on states for an initial separation of 2 nm;

FIG. 13 shows a plot of a calculated range of initial separations for arange of device sizes which yield bistable devices for a hard materialsuch as silicon;

FIG. 14 shows a plot of a calculated range of initial separations for arange of device sizes which yield bistable devices for soft organicmaterials;

FIG. 15 shows calculations of ET for switching a 20 nm device on (FIG.15A) and off (FIG. 15B);

FIG. 16A shows current-voltage (I-V) measurements made on lower (bound)and upper (supported) nanotubes of a typical device showing ohmicbehavior with resistances of 11 and 58 kΩ;

FIG. 16B shows current-voltage (I-V) measurements made on lower (bound)and upper (supported) nanotubes of a typical device showing ohmicbehavior with resistance of 112 kΩ; and

FIG. 17 shows a plot of device state (on) and (off) vs. resistance.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a series of techniques and devicesinvolving nanoscopic-scale wires, also referred to herein as “nanoscopicwires”. “Nanoscopic-scale” or “nano” is meant to include elements ofwidths or diameters of less than 1 μm. Nanotubes are used as one exampleof small wires for use in the invention and, in preferred embodiments,devices of the invention include wires of scale commensurate withnanotubes. A “wire” refers to any material having a conductivity of anysemiconductor or any metal.

One significant aspect of the invention involves electronic memoryelements in which crossbar junctions (the intersections of crossedwires) are defined by at least one nanoscopic-scale wire. These crossbarjunctions themselves can serve as both diode or memory elements of thedevice and as elements for switching between different states (“on” and“off” states). That is, a crossbar array device is provided in which oneor more, preferably all, elements are free of auxiliary circuitrydefining the elements. Current silicon based devices require atransistor and capacitor to store a bit in dynamic RAM, or four to sixtransistors are required to store a bit in static RAM. The presentdevice is free of auxiliary circuitry, such as transistors andcapacitors, addressing the elements to switch them between states. Thisis described more fully below. Of course, “free of auxiliary circuitrydefining the elements” does not encompass electrodes and power sourcesor other macroscopic elements required to operate the device which areoutside the nanoscopic memory element array.

In all of the exemplary embodiments described herein, circuitryincluding at least one nanoscopic-scale wire is described. Nanotubes, inparticular carbon nanotubes, are primarily described and shown asexamples of nanoscopic-scale wires. While nanotubes, and in particularcarbon nanotubes, are preferred for use in the invention, anynanoscopic-scale wires can be used, including nanoscopic wires such asnanorods, nanowires, organic and inorganic conductive and semiconductingpolymers, and the like. Other conductive or semiconducting elements thatmay not be molecular wires, but are of various small nanoscopic-scaledimension, also can be used in some instances (described more fullybelow), e.g. inorganic structures such as main group and metalatom-based wire-like silicon, transition metal-containing wires, galliumarsenide, germanium, cadmium selenide structures, thin metal wiresformed by lithographic techniques, and the like. A wide variety of theseand other nanoscopic-scale wires can be grown on and/or applied tosurfaces in patterns useful for electronic devices in a manner similarto techniques described herein involving nanotubes, without undueexperimentation. The criteria for selection of nanoscopic-wires andother conductors or semiconductors for use in the invention are based,in some instances, mainly upon dimension to achieve high-density memorydevices, and in other instances based on dimension and robustness. Thewires should be able to be formed of at least one micron, preferably atleast three microns, more preferably at least five microns, and morepreferably still at least ten or twenty microns in length, andpreferably are less than 100 nanometers, more preferably less than 75nanometers, and more preferably less than about 50 nanometers, and morepreferably still less than about 25 nanometers in thickness (height andwidth). The wires should have an aspect ratio (length to thickness) ofat least about 10:1, preferably greater than about 1000:1. Selection ofsuitable conductors or semiconductors, including nanoscopic wires, willbe apparent and readily reproducible by those of ordinary skill in theart with the benefit of the present disclosure.

A preferred nanoscopic-scale wire (i.e. nanoscopic wire) for use indevices of the invention can be either a nanotube or a nanowire.Nanotubes (e.g. carbon nanotubes) are hollow. Nanowires (e.g. siliconnanowires) are solid. Whether nanotubes or nanowires or other nanoscopicscale wires are selected, it is preferred that they be selected amongthose that are robust.

The invention facilitates reliable connection of input/output electroniclines to nanoscopic devices in a highly integrated system such that thestate of the device, or individual junctions, is readable in thepresence of many other connected elements. System architectures of theinvention are defect and/or fault tolerant. Single wall nanotubes(SWNTs) are particularly preferred as they exhibit unique structural,electronic, and chemical properties that are particularly suitable formolecular electronics. Structurally, SWNTs are formed of a singlegraphene sheet rolled into a seamless tube with a diameter on the orderof 0.5-5 nm and a length that can exceed 10 microns. Depending ondiameter and helicity, SWNTs can behave as one-dimensional metals orsemiconductor and are currently available as a mixture of metallic andsemiconducting nanotubes. Methods of manufacture of nanotubes, includingSWNTs, and characterization are known. Methods of selectivefunctionalization on the ends and/or sides of nanotubes also are known,and the present invention makes use of these capabilities for molecularelectronics. The basic structural/electronic properties of nanotubes canbe used to create connections or input/output signals, and nanotubeshave a size consistent with molecular scale architecture.

Structural and/or chemical changes associated with preferrednanoscopic-scale wires used in the invention can modulate the propertiesof the wires and create electronic devices of a variety of types. Inaddition, covalent and noncovalent chemistry can be used to direct, withmolecular precision, the assembly of these wires into structures on amassively parallel scale.

Preferred nanoscopic wires of the present invention also are individualnanotubes, preferably individual SWNTs. As used herein, “individualnanotube” means a nanotube free of contact with another nanotube (butnot excluding contact of the type desired between individual nanotubesin a crossbar array or other electronic device, as described herein).Typical individual nanotubes can have a thickness as small as 0.5 nm.This is in contrast to nanotubes produced primarily by laservaporization techniques that produce high-quality materials, butmaterials formed as ropes having diameters of 2-50 nanometers or moreand containing many individual nanotubes (see, for example, Thess, etal., “Crystalline Ropes of Metallic Carbon Nanotubes” Science 273,483-486 (1996), incorporated herein by reference). While nanotube ropescan be used in the invention, individual nanotubes are preferred.

The invention preferably utilizes metal-catalyzed CVD to synthesize highquality individual nanoscopic-scale wires such as nanotubes formolecular electronics. CVD synthetic procedures needed to prepareindividual wires directly on surfaces and in bulk form are known, andcan readily be carried out by those of ordinary skill in the art. See,for example, Kong, et al., “Synthesis of Individual Single-Walled CarbonNanotubes on Patterned Silicon Wafers”, Nature 395, 878-881 (1998);Kong, et al., “Chemical Vapor Deposition of Methane for Single-WalledCarbon Nanotubes” Chem. Phys. Lett. 292, 567-574 (1998), bothincorporated herein by reference.

One aspect of the present invention provides an article comprising anelectrical crossbar array comprising at least two crossed wires. Thearray can comprise an n×m array in which n and m can be the same ordifferent and each is an integer greater than 0. Thus, at least twocrossed wires can comprise a 1×1 array or a much larger array. At leastone of the crossed wires is a nanoscopic wire. For ultra-dense arrays,it is preferred that all of the wires in the array are nanoscopic wiresto provide small device sizes. Other devices, however, may not requiresuch ultradense arrays and to reduce costs, non-nanoscopic wires can beused in conjunction with nanoscopic wires. Alternatively, nanoropes canbe used exclusively or in conjunction with nanotubes.

FIG. 8 shows an example of a crossbar array of the present invention. InFIG. 8, crossbar array 200 comprises wires 201-204 supported, by variousmeans, on a substrate comprising a thin dielectric layer 214 (e.g.,SiO₂) which terminates conducting layer 215 (e.g., highly dopedsilicon). Wire 203 is parallel to wire 204 and these are crossed withparallel wires 201 and 202. FIG. 8 shows wires 201 and 202 perpendicularto wires 203 and 204, and typically this arrangement provides highsymmetry, allowing facile integration with other systems. Of course,wires do not have to be crossed at 90° angles and can be crossed at anyangle as desired.

At least two crossed wires can define a junction, e.g., wire 201 isdisposed adjacent wire 203 at junction 206. “Disposed adjacent” does notrequire that wires 201 and 203 be in contact with each other, but ratherthat wires 201 and 203 are positioned relative to each other such thatthey are capable of contacting each other. The wires can be free ofcontact with no other material intermediate the wires, or spacingbetween the wires can be provided with the aid of intermediary material(for example, see FIGS. 5 and 6 and accompanying discussion). Theability of the crossed wires to contact and release from each otherreversibly at cross point junctions provides the basis for addressableelements, such as switches, memory elements and diode junctions.

In one embodiment, wires 203 and 201 are disposed adjacent each other bypositioning wire 203 directly on substrate 214. Wire 203 (and 204) isreferred herein as an example of a “bound” wire. Wire 203 isintermediate substrate 214 and wire 201. Wire 201 is supported abovewire 203, relative to substrate 214, by supports 210. Wire 201 (and 202)is referred herein as an example of a “supported” wire. Supports 210 canbe spaced periodically on either side of each bound wire (e.g., wires203 and 204). This arrangement of supports 210 allows each junction(e.g., junctions 206 and 207) to be addressed independently of eachother.

In another embodiment, wires 201 and 203 can be disposed adjacent eachother by positioning wire 203 in a trench. Referring to FIG. 10B, device230 features parallel trenches 232. Bound wires are nested in each oftrenches 232 which are of sufficient depth to prevent the bound wiresfrom projecting above substrate surface 235. A parallel array of crossedwires 233 can be positioned across trenches 232. Again, bound andsupport wires should have sufficient spacing from each other to allowcontact with each other and release from each other at junctions.

Referring back to FIG. 8, at least one end of each of wires 201-204 isin electrical contact with one of contact electrodes 212. That is, inone embodiment, at least one wire is attached to the contact electrode.The attachment can be provided by covalently attaching at least one wireto the contact electrode. The electrode can comprise any materialcapable of electrical conduction, as is known in the art.

FIG. 8 shows wires 201 and 203 not in contact, i.e., free of contact,with each other. “Free of contact” refers to a sufficient gap betweencrossed wires such that there is no conduction pathway between wires 201and 203. Supported wires such as wire 201 preferably are selected topossess a stiffness to allow periodic support above, yet free of contactwith, wire 203.

In contrast, wires 201 and 204 are in contact with each other atjunction 207. “Contact” can refer to electrical contact, in which thereis a conduction pathway between wires 201 and 204, or in van der Waalscontact with each other. Often, for conducting wires, van der Waalscontact provides electrical contact. To achieve such contact, wire 201is capable of deformation localized at a region around junction 207.Thus, the wire of the present invention should have a sufficient Young'smodulus such that the wire is capable of deformable van der Waalscontact with the crossed wire at junction 207. In addition, thisdeformation occurs without affecting neighboring junctions, i.e., wiresat neighboring junctions can independently undergo deformation or remainfree of contact with a crossed wire.

It is another feature of the array of the present invention thatdeformation occurs via application of a stimulus. Typically, thestimulus is an electrical stimulus as provided through the at least oneelectrode 212. A stimulus can comprise biasing the two crossed wireswith opposite polarities such that electrical attraction causes wire 201to deform towards wire 207. In addition, wires 201 and 204 preferablyare selected to have sufficient adhesion energy to maintain deformablevan der Waals contact upon removal of the stimulus. Thus, no appliedenergy is required in preferred embodiments to maintain wires 201 and204 in contact with each other. The benefits of this capability arediscussed below with respect to the potential for the crossbar array ofthe present invention to provide bistable (i.e. non-volatile) elements.

It can be seen that bound wires 203 and 204 do not require deformationof any type. Supported wires 201 and 202, however, should havesufficient stiffness to remain supported above bound wires, yet havesufficient flexibility to enable deformation to contact the bound wireswithout breaking and have sufficient adhesion energy to maintain van derWaals contact. Furthermore, supported wires 201 and 202 should be ofsufficient robustness to withstand the strain of several deformationprocesses. Carbon nanotubes possess all these properties and are apreferred material for supported wires of the crossbar array. Of course,carbon nanotubes can be used as the bound wires. In addition, thesupported wires should have enough friction to prevent slippage onsupports, particularly during deformation processes. The interactionwith the support could be further enhanced through chemicalmodification, if required, although this is not always necessary.

A device that is capable of maintaining at least two different states,e.g., contact between crossed wires or lack of contact between crossedwires without the need for applied energy to maintain either state, isreferred to as a “bistable” device. As an example, bistable deviceelements provided by the invention at junctions of crossbar arrays willnow be described. Bistable elements of the invention include those inwhich each of the two states is stable or metastable. These bistableelements have, as a common feature, nanoscopic scale electromechanicalswitching between “on” and “off” states where the “on” state involvesnanoscopic-scale wires in electrical contact at the crossbar junctionand in the “off” state the nanoscopic-scale wires are free of electricalcontact (separated). Reading the “on” or “off” state of any crossjunction is easily accomplished by measuring the resistance/conductanceof the junction. The two states in this device architecture can beeasily distinguished independent of fluctuations in the “on” stateresistance. The “off” state conductance is lower than a conductance ofthe “on” state to an extent limited only by detection sensitivity, fortypical bistable structure parameters. For example, for carbon nanotubescalculations suggest a change in “on” to “off” state resistance by afactor of 10³ to 10⁶ for typical device parameters (i.e. for typicalnanotube separations in the “off” state). The device architecture andfunction is thus highly robust.

The operation of bistable switching elements of the invention now willbe described with reference to FIG. 2. FIG. 2 shows arrangement 26 and28, each including a crossbar array junction 32. With reference toarrangement 28 of FIG. 2, the “off” state is at mechanical equilibrium,i.e. when the crossed nanotubes are separated as illustrated. As avoltage is established between wires 18 and 30 that attracts them toeach other, wire 30 is deflected towards wire 18 and contacts wire 18,defining the “on” state, corresponding to van der Waals contact. Theconduction between the crossing nanoscopic wires is either high or lowin the “on” and “off” states, respectively. In the “on” state, theconduction is defined by the approximate constant wire/wire contact atthe cross. In the “off” state, conduction occurs by quantum mechanicaltunneling and will be much lower. The bistable device includes stableminima at both the “off” and “on” states by virtue of mechanicalequilibrium and van der Waals contact, respectively, and can be switched“on” by biasing the nanotubes with opposite polarity. The electrostaticterm lowers the potential minimum at contact and ultimately eliminatesthe barrier between “off” and “on” states to enable switching. Removalof the potential leaves the system in a stable “on” state. The devicecan be switched to the “off” state in a similar manner by applying thesame potential to both tubes. Switching between the “on” and “off”states at reasonable (approximately 4-5 Volts) potentials isfacilitated. A second general class of electromechanical switches (e.g.arrangement 26 of FIG. 2) are based on crossbar SWNT arrays that areinitially in a contact “on” state at rest, but when electrostaticallyseparated enter a second potential “off” minimum.

Nanoscopic-scale devices of the invention can exhibit switching times onthe order of 6-30 picoseconds, thus they can operate at a frequency ofas high as about 200 GHz. Thus, the invention encompasses low frequencydevices also. Moreover, the energy to switch an individual device isextremely small. Much lower power is required than for silicon DRAMs atsimilar frequencies. Additionally, nanotubes have extremely good thermalconductivity along their tube axes and thus are an ideal structure forremoving heat from a highly integrated device.

In addition, the nanoscopic-scale device of the present inventiondisplays stability at a wide range of temperatures, limited only by thestability of the metal contacts. For example, memory elements providedfrom carbon nanotubes exhibit an intrinsic thermal stability up to orhigher than 1000° C. The memory elements also exhibit radiationstability and non-volatility of the stored information.

FIG. 4 illustrates, schematically, energy curves associated with “on”and “off” states of a memory element 32 of a device according to oneembodiment of the invention in which a first electronic conductor issuspended above and free of contact with a second electrical conductorin its lowest energy configuration (e.g. arrangement 28 of FIG. 2).Curve 51 represents the energy states in the various conformations. Thelowest energy configuration at mechanical equilibrium is the “off” statewhere the crossed conductors are separated. The “on” state correspondsto a Van der Waals contact. Conduction between the crossed wires is highin the “on” state and low in the “off” state. Switching is carried outas follows. Switching from the “off” state to the “on” state (followingthe energy plot of curve 56) is carried out by biasing the wires 18 and30 with opposite polarity so that they are attracted toward each otheruntil reaching a stable Van der Waals contact distance (Z_(vdw)).Switching “off”, following the energy plot of curve 54, is accomplishedby biasing wires 18 and 30 with the same polarity so that they repeleach other, moving toward their mechanical equilibrium distance (Z₀).The device of the invention is highly efficient in that switchingbetween “off” and “on” states can be carried out at approximately 4-5volts, and no external power is required to maintain the wires in eitherthe “on” or “off” states (i.e. bistable, non-volatile).

The “off” and “on” states can be read easily by measuring a resistanceof the junctions. In one embodiment, a difference between the resistancebetween two crossed wires must be sufficient to differentiate betweenthe “on” and “off” position.

One aspect of the invention involves the spatially-controlled formationof nanoscopic-scale wires into well-defined crossbar arrays. Two generaltechniques for spatially-controlled formation are described herein, oneinvolving directed assembly of pre-formed nanoscopic-scale wires onto asurface in a desired pattern, and the second involving growth ofnanoscopic-scale wires on a surface in a desired pattern directed, forexample, by electric fields, highly-directional precursor flow rates(“precursor wind”), template-directed growth (growth within hostchannels; mechanically-directed growth), growth and assembly within hostmaterials such as self-assembled block copolymers, inorganic hoststructures, and the like. Relatively simple (1×1) crossbar arrays areprovided in addition to more highly integrated arrays, for example, 1×8,8×8, 16×16 arrays, etc. The arrays can serve as memory devices, wherejunctions of the arrays can function as memory elements. Alternatively,the junctions can serve as diodes, for overcoming problems such ascross-talk, as described below.

Referring now to FIG. 1, a technique for directed assembly of apre-formed nanoscopic wire onto a chemically patterned surface isillustrated schematically. In FIG. 1 a silicon/silicon dioxide substrate10 is provided and coated with a self-assembled monolayer (SAM) 12 ofalkylsilane, uniformly. In one example of patterning the SAM fordirected assembly of hanoscopic scale circuitry atomic force microscopy(AFM) then is used to write, at high resolution, a pattern in SAM 12 atwhich the SAM is removed. The pattern can be for example linear, or acrossed array of lines linear in embodiments for making nanoscopiccrossed arrays. As illustrated, the pattern is linear and results in alinear patterned SAM 14 on substrate 10 defining lines of alkylsilaneseparated by a linear region free of SAM. In another technique,microcontact printing can be used to apply patterned SAM 14 to substrate10. Microcontact printing is described below.

Next, open areas in the patterned surface (the SAM-free linear regionbetween linear SAM 14) is filled with an amino-terminated SAM thatinteracts in a highly specific manner with a nanoscopic wire such as ananotube. The result is a patterned SAM, on substrate 10, includinglinear SAM portions 14 of methyl terminated material (methyl groupsexposed at the surface) separated by a line 16 of amino-terminated SAMmaterial. Of course, any desired pattern can be formed where regions ofthe amino-terminated SAM material corresponds to regions at which wiredeposition is desired. The patterned surface then is dipped into asuspension of wires, e.g. nanotubes, and rinsed to create an array inwhich wires 18 are located at regions 16 of the SAM. Where nanotubes areused, an organic solvent such as dimethyl formamide can be used tocreate the suspension of nanotubes. Suspension and deposition of othernanoscopic-scale wires is achievable with easily selected solvents.

Any of a variety of substrates and SAM-forming material can be usedalong with microcontact printing techniques, such as those described ininternational patent publication WO 96/29629 of Whitesides, et al.,published Jun. 26, 1996 and incorporated herein by reference. PatternedSAM surfaces can be used to direct a variety of nanoscopic wires ornanoscopic-scale electronic elements. SAM-forming material can beselected, with suitable exposed chemical functionality, to directassembly of a variety of electronic elements. Electronic elements,including nanotubes, can be chemically tailored to be attractedspecifically to specific, predetermined areas of a patterned SAMsurface. Nanotubes are particularly suitable for chemicalfunctionalization on their exterior surfaces, as is well known.

Chemically patterned surfaces other than SAM-derivatized surfaces can beused, and many techniques for chemically patterning surfaces are known.Suitable exemplary chemistries and techniques for chemically patterningsurfaces are described in, among other places, international patentpublication serial no. WO 97/34025 of Hidber, et al, entitled,“Microcontact Printing of Catalytic Colloids”, and U.S. Pat. Nos.3,873,359; 3,873,360; and 3,900,614, each by Lando, all of thesedocuments incorporated herein by reference. Another example of achemically patterned surface is a micro-phase separated block copolymerstructure. These structures provide a stack of dense lamellar phases. Acut through these phases reveals a series of “lanes” wherein each lanerepresents a single layer. The block copolymer is typically analternating block and can provide varying domains by which to dictategrowth and assembly of a nanoscopic wire.

While FIG. 1 illustrates, schematically, assembly of a nanoscopic wireon a SAM in a pattern dictated by the SAM, and a SAM defining adelineated pattern with a nanoscopic wire associated with theself-assembled monolayer, FIG. 2 illustrates, schematically, creation ofa crossed microscopic wire array using self-assembled monolayer patterndirection. In FIG. 2 a substrate 10 including a SAM pattern havingportions 14 and 16, as described with reference to FIG. 1, and amicroscopic wire 18 formed on portion 16 of the SAM is illustrated. AFMor another technique (e.g., electron-beam lithography, etc.) can be usedto write a linear pattern orthogonal to the original wire orientation inregions 20 of sections 14 of the SAM. Next, the open areas in thepatterned surface are filled with amino-terminated SAM of the samelength (amino-terminated SAM sections 22) or greater length (SAMsections 24) compared to the original SAM pattern. This results in anarrangement 26 in which all SAM material is of the same height, or anarrangement 28 in which portions of the SAM arrangement extend above theplane of the original SAM and, optionally, above the height of the wire18 to provide clearance above the wire. The patterned surface then isdipped into a suspension of additional nanoscopic-scale wires and rinsedto create a crossbar array. In arrangement 26 a wire 30 is arranged incrossbar array formation across original wire 18 at junction 32, incontact with wire 18. Arrangement 28 defines an electrical crossbararray comprising at least two nanoscopic wires in crossbar arrayorientation, where the crossbar array is made up of wires that are notin contact with each other at the junction. These arrangements can beused directly as a bistable device memory element, as will be apparentto those of ordinary skill in the art with the benefit of thedescription below.

Described above are techniques for assembly of pre-formednanoscopic-scale electronic elements onto a surface. Another generaltechnique included in the invention for creation of nanoscopic-scaleelectronic devices involves directed growth of nanoscopic-scale elementson a surface in a predetermined pattern. FIGS. 3A and 3B illustrate,schematically, one such technique involving formation of crossbar arraysvia CVD in the presence of electric fields. In FIG. 3A, an array ofcatalytic sites 34 are arranged opposite each other and define desiredend points of parallel nanoscopic wires of a crossbar array (althoughpairs of catalytic sites are illustrated, as described below only onecatalytic site per wire is needed). Clusters 34 are used to direct thegrowth of bridging nanoscopic-scale wires in a direction in the presenceof an electric field. An electric field is oriented in a directionparallel to (in the direction of) the desired direction of wire growthusing electrodes 36 and 38, connected by an electrical circuit 40,oriented behind each array of the diametrically opposed catalytic sites.The underlying basis for the technique is that the energy of apolarizable, anisotropic structure such as a nanoscopic-scale wireformed in accordance with the invention is lower when its long axis isaligned with the field. Correspondingly, when an anisotropic structureis misaligned, there is a force exerted on the structure to bring itinto alignment. This basic concept of electric field alignment has beenused previously for the alignment of anisotropic molecules throughmicron scale fibers, and thus the technique will be understood by andreproducible by those of ordinary skill in the art with the benefit ofthe instant disclosure. The highly anisotropic, or one-dimensional,structure of nanotubes, especially SWNTs, leads to a much greaterpolarization anisotropy (exceeds 1,000:1 along the tube axis) than wouldbe present for a three-dimensional material of similar dimensions (forexample, a copper nanowire), thus nanotubes are particularly preferredfor this technique. This will lead to greater energy/force terms for thenanotube aligned with the field. Any slight misalignment with the fieldduring nanotube growth is corrected as the force acting to re-orient itwith the field becomes increasingly large as the nanotube grows. Analternative mechanism, for aligning nanotubes growing from an electrodeis the accumulation of a net charge on a nanotube and electrostaticattraction to an oppositely biased electrode. According to thetechnique, the array of diametrically opposed catalytic sites 34, in thepresence of an electric field produced by circuit 40 and electrodes 36and 38, is exposed to conditions of chemical vapor deposition allowinggrowth of a nanotubes 42 between the catalytic sites.

Re-orientation of the structure such that a series of catalytic sites 44are diametrically opposed in a direction perpendicular to catalyticsites 34, with creation of an electrical field in a directionperpendicular to nanotubes 42, and exposure to chemical vapor depositionconditions results in deposition of nanotubes 46 aligned in crossbararray orientation perpendicular to nanotubes 42.

Catalyst sites for growing nanoscopic wires can be patterned bylithographic techniques, self-assembly with or without host phases, orpatterning via proximal probes (e.g. dip pen lithography).

As mentioned, only one catalyst site per wire is required. Withreference to FIG. 3A, one set of catalytic sites 34 can be provided and,in the presence of an electric field and exposure to conditions of CVDnanotubes can be grown from each catalytic site extending away from eachsite in the same direction to form an array of nanotubes 42 asillustrated. Similarly, with reference to FIG. 3B, only one set ofcatalytic sites 44 is required. As mentioned above also, othertechniques for directing growth of nanoscopic-scale wires can be usedsuch as highly-directional precursor flow rates, template-directedgrowth, growth within host materials, etc.

A combination of techniques to form crossbar arrays of the invention canbe used. With reference to FIG. 2, wires 18 can be formed by anytechnique, including conventional lithographic techniques. Then,directed growth of nanoscopic-scale elements can take place across SAMsections 22 or 24 resulting in arrangements 26 and 28, respectively.

Nanoscopic wires can also be formed on a surface in a pattern dictatedby a mechanically patterned surface. Mechanically patterned surfaces canbe provided by walls, channels, trenches, capillaries or the like.Referring back to FIG. 10, article 220 features a plurality of paralleltrenches 222 which can be provided in a substrate surface by a varietyof means, including lithographic techniques, microcontact printing,nano-imprinting, nano-machining, etching, whether by chemical etching,laser etching, or by a focused ion beam (FIB) machine, and relatedtechniques. Alternatively, some substrates, such as vicinal surfaces orlattice mismatched hetero-epitaxial structures inherently exhibit suchtrenches, and thus can also be used as article 220. Article 220 featurestrenches 222 milled by an FIB. The trenches can serve as a mechanicalguide for the growth of nanowires, such as by CVD growth techniques.Crossed wires 233 (FIG. 10B) can be grown by providing a plurality ofcatalyst nanoparticles 224 (i.e., catalytic sites, FIG. 10A) linearlydisposed parallel to trenches 222 and along an edge of article 220. FIG.10B shows how growth of nanowires 233 can be directed from sites 234over trenches 232 by techniques such as CVD. The growth can be directedunder a local electric field parallel to the surface. The origin ofgrowth is defined by the patterning the catalyst nanoparticles.

Another example of wire growth along a substrate involves an articlehaving a plurality of indentations and protrusions. By positioningprotrusions on the substrate surfaces, cavities are formed and definedby the substrate surface and the plurality of indentations. Theseindentations can have the shape of capillaries. The capillary walls canbe used to mechanically direct growth originating from a catalytic siteor can be used to chemically pattern a surface which in turn directsgrowth of the nanowire.

Nanoscopic wires can also be formed on a surface in a pattern dictatedby gas flow. For example, disposing a series of catalyst nanoparticles(i.e., catalyst sites) and subjecting these nanoparticles to a gas flowof high pressure can direct growth of a nanowire in the direction of gasflow. Particularly, this method provides a novel growth technique wherethe gas comprises a reactant for the nanowire. For example, carbonprecursor gases such as ethylene, acetylene, methane or carbon monoxidecan be used to grow carbon nanotubes whereas silane can be used to growsilicon nanowires. Other precursors are also well known in the art.

Referring again to FIGS. 3A and 3B, through placement of catalytic sites34 and 44 adjacent a series of contact electrodes (not shown), or use ofthe catalytic sites 34 or 44 as contact electrodes where they areelectrically conductive and provide good electric contact withnanotubes, each of the nanotubes can be provided in electrical contactwith a different contact electrode. Covalent attachment betweennanotubes and contact electrodes is preferred, and is easily facilitatedby functionalizing the nanotubes, at their ends, with a molecule thatcan attach, preferably covalently, to a contact electrode.Functionalization of nanotubes is known, and functional groups thatattach to materials that can serve as contact electrodes are known, thusthe technique of the invention is readily facilitated based on theinstant disclosure. In one embodiment, the ends of the nanotubes arefunctionalized with conjugated thiols, and the contact electrodes aregold. See, for example, Wong, et al., “Covalently FunctionalizedNanotubes as Nanometer Probes for Chemistry and Biology” Nature 394,52-55 (1998); Wong, et al., “Covalently-Functionalized Single-WalledCarbon Nanotube Probe Tips for Chemical Force Microscopy” J. Am. Chem.Soc. 120, 8557-8558 (1998), both incorporated herein by reference. Theend states of the nanotube can effectively couple to bulk conductionchannels in the nanotubes as described by Kim, et al., “ElectronicDensity of States of Atomically-Resolved Single-Walled Carbon Nanotubes:Van Hove Singularities and End States” Phys. Rev. Lett. 82, 1225-1228(1999), incorporated herein by reference.

Using the techniques of the invention it is possible to achieve anactive element two-dimensional density of as high as about 10¹² memoryelements/cm². Thus, low or high density arrays are envisioned. Theseelement can be used to construct non-volatile random access memory(RAM), read-only memory bits and configurable logic, among otherapplications. This is facilitated where an array of nanoscopic wires 42(FIG. 3B) are positioned at 20-nanometer intervals. Where wires 46 aresimilarly arranged, this density is achieved. By using nanoscopic wiressuch as nanotubes of 10 micron length, with a memory element every 20nanometers along each nanotube, an array can be formed with at least 500parallel wires in each direction, each wire containing at least 500crossbar array junctions (memory elements). At least 250,000 memoryelements can be formed in such an array. Three-dimensional arrays can becreated as well, and can have higher integration densities thantwo-dimensional arrays. Three-dimensional arrays are produced usingmulti layer architecture extended from that described above withreference to FIG. 2 or from assembly using block polymers as directingagents.

As mentioned above, the invention provides a series of memory elementsin a crossbar array that can be written and read (switched between “on”and “off” settings) without auxiliary circuitry addressing each element.For example, FIG. 5 shows element 32 is a bistable element in that it isstable in both the “on” and “off” states, and free of auxiliaryelements, such as capacitors, transistors and switches.

Referring now to FIG. 5, a stable/metastable memory element 32 accordingto arrangement 26 of FIG. 2 is illustrated, schematically andgraphically. As illustrated, two touching crossed wires 18 and 30 in the“on” state are biased against an underlying ground. Curve 70 representsthe energy states in the various conformations. Switching “off” (curve74): when the wires are biased with similar polarity, they are repelledfrom each other and spatially separated. They can rapidly return to ametastable distance where they are separated by space or molecules 72filling the gap between them. This metastable “off” state slowly relaxesback to the “on” state within a retention time. Switching “on” (curve76): when the nanotubes are biased with opposite polarity, they attracteach other, accelerate their relaxation to a van der Waals contactdistance. FIGS. 6A-6C illustrate various embodiments in which oppositelycharged molecules are allowed to organize within cross junctions betweennanotubes in the “off” state according to the arrangement of FIG. 5.These molecules can include short charged polymers 60 (FIG. 6A),surfactant molecules 62 that can form micellar structures aroundnanotubes (FIG. 6B), polymer brushes 64 grafted to a SAM that forms abasis of the structure (FIG. 6C), and the like.

Another aspect of the invention provides an article comprising anelectrical crossbar array comprising at least two crossed wires defininga diode. The device is free of auxiliary circuitry other than the atleast two crossed wires defining the diode. For example, if bound wiresare semiconducting and support wires are metallic conductors, contactbetween the two wires will provide a metal/semiconductor junction, whichfunctions as a rectifying Schottky diode at the contact junction. Thus,an on junction provides intrinsic rectifying behavior. Currently,nanotubes exist as a mixture of semiconductor and metallic conductornanotubes. It has not been possible to separate the mixture into purelysemiconducing nanotubes and metallic nanotubes. Rectifying junctions canalso be provided by providing semiconductor nanowires, preferablyn-type. For metallic nanotubes, a rectifying Schottky junction willresult in the “on” state while for semiconducting nanotubes (which areintrinsically p-type) a rectifying p/n diode junction will result if thesemiconducting nanowire is n-type doped.

The provision of diode junctions can eliminate the problem of cross talkin crossbar arrays. FIG. 9A shows an example of a 2×2 array in which bit[21] is off. Thus, a direct conducting path between bit [21] and bit[11] is not acceptable. Because there is no restriction on a directionfor a conduction pathway, a pathway as represented by bold line 250 cancircumvent the [21]/[11] pathway. This will cause bit [21] to appear oneven though it is off. FIG. 9B shows a result of rectifying behaviorwhen one set of crossed wires comprises a semiconductor and the otherset of crossed wires comprises a metallic conductor. Conducting islimited to one direction only and cross talk is thus prevented.

As mentioned previously, providing pure semiconductor nanotubes ormetallic nanotubes has not been possible to this point. Thus, anotheraspect of the present invention provides a method involving a mixture ofmetallic nanotubes and semiconducting nanotubes. The method involvesseparating the metallic nanotubes from the semiconducting nanotubes. Itis known that metallic nanotubes have a greater polarizability thansemiconducting nanotubes by about three orders of magnitude. Thus, inone embodiment, the step of separating the mixture involves subjectingthe mixture to an electric field of intensity sufficient to selectivelyorient metallic nanotubes. Depending on the intensity of electric field,there is a critical length below which only metallic nanotubes will bealigned. Thus, the intensity can be adjusted to be in accord with afield below the critical length. Above this critical length, both typesof nanotubes can be aligned by the field. Below this length, theelectric field is of an intensity such that the semiconducting nanotubesremain unoriented with respect to the electric field. Once selectivealignment is achieved, separation is routine.

As noted above, it is a significant advantage of the invention thatjunction elements can be switched between “on” and “off” statesremotely, i.e., by simply addressing at least one end of each of thewires that cross to form the memory element (wires 18 and 30 in FIGS. 2and 4). Where the junction elements comprises memory elements, ordiodes, some or preferably all of the memory elements are free ofauxiliary circuitry defining the memory or diode elements and free ofauxiliary circuitry addressing the memory or diode elements to switchthem between states; the memory or diode element simply includes wires18 and 30 that define the lead wires addressing the memory or diodeelement. Those of ordinary skill in the art will understand the meaningof auxiliary circuitry for switching a memory or diode element between“on” and “off” states, auxiliary circuitry defining memory statesthemselves, and the meaning of a device free of these components. Anexample of auxiliary circuitry defining memory states themselvesincludes an electrical pathway connecting two crossed conductors at ajunction that can be switched from a conducting state to anon-conducting state. An example of auxiliary circuitry for switching amemory element between states includes circuitry connected to theelectrical pathway that can be switched to render the pathway conductingor non-conducting.

One feature of the invention is that, with reference to FIG. 2,nanoscopic-scale wires 18 and 30 need not each be flexible nanoscopicwires such as nanotubes. As can be seen from the illustration anddescription relating to FIGS. 4 and 5, memory elements of the inventioneach include one wire (wire 18 in FIGS. 4 and 5) that need not moveduring switching, and can be made of essentially any material havingappropriate conductivity that can be formed in the appropriatedimensions. Although nanotubes and other nanoscopic wires can be usedfor fixed wires 18, wires formed by more conventional techniques such aslithography can be used as well. Wire 30 should be selected to meet theadditional requirement of repeated flexure during switching between“off” and “on” states, as illustrated. Wire 30 should thus be selectedto have elasticity and robustness to meet this demand. Nanotubes exhibitsuch robustness and are ideal for use as flexing wires 30 in theinvention. Thus, devices of the invention can be constructed entirely bydirected assembly of pre-formed wires onto a surface or entirely fromdirected growth of wires at a surface, or a combination, or fixed wires18 can first be formed via a conventional technique such as lithographyfollowed by placement of flexing wires 30 by directed assembly, ordirected growth.

Referring now to FIG. 7, a cut away schematic illustration of a crossbararray 80 of the invention is presented. Array 80 includes a series ofparallel, equally-spaced wires 82, 84, 86, 88 . . . , and a series ofparallel, equally-spaced wires 100, 102, 104, 106 . . . that cross (areperpendicular to) wires 82, 84 . . . . Each of wires 82, 84, 86 . . . isaddressed by an electrode 120, 122, 124 . . . at one end thereof andeach of wires 100, 102, 104, 106 . . . is addressed by an electrode 140,142, 144 . . . : at one end thereof. It is a feature of the inventionthat wires 82, 84, 86 . . . and wires 100, 102, 104 . . . requireelectrical contact with only one electrode, i.e., one interconnect canbe used to address many individual junctions. Electrodes can be providedat opposite ends of the wires from those ends at which electrodes areshown (opposite ends not shown in FIG. 7), but this is optional. Each ofwires 82, 84, 86 . . . crosses each of wires 100, 102, 104 . . . , eachcrossed wire junction defining a memory element as illustrated in FIGS.2, 4, and 5 and discussed above. For example, junction 160 is a memoryelement defining the intersection of wires 88 and 104. When device 80 isconstructed of memory elements as illustrated in arrangement 28 of FIG.2, and in FIG. 4, at mechanical equilibrium wires 88 and 104 are free ofcontact and element 160 is “off”. Biasing electrodes 126 and 144 atopposite polarity brings wires 88 and 104, at junction 160, into contactwith each other (stable Van der Waals contact) and junction 160 isswitched “on”. Bias need not be maintained between electrodes 126 and144 to maintain element 160 in the “on” state in preferred embodiments.To switch element 160 “off”, electrodes 126 and 144 are biased with thesame polarity to repel wires 88 and 104 from each other at junction 160.Where device 80 includes junctions as illustrated in arrangement 26 ofFIG. 2 and FIG. 5, at mechanical equilibrium junction 160 is in the “on”state with wires 88 and 104 contacting each other, and element 160 isswitched “off” by biasing electrodes 126 and 144 at similar polarity.Switching element 160 back “on” is accomplished by biasing electrodes126 and 144 at opposite polarity.

Another aspect of the present invention provides an article comprisingan electrical crossbar array comprising at least two crossed nanoscopicwires defining a memory element capable of being switched irreversiblybetween at least two readable states. Thus, the device is “read-only”.In another embodiment, the article comprises an electrical crossbararray comprising at least two crossed nanoscopic wires defining a memoryelement capable of being switched reversibly. Thus, the devices can beused for a volatile RAM (e.g. require a power supply to keep the storedinformation) or a non-volatile RAM.

EXAMPLE 1

To quantify the bistability and switching behavior of the device elementa total energy, ET, can be calculated:E _(T) =E _(vdw) +E _(elas) +E _(elec)  (1)

where E_(vdw) is the van der Waals (vdW) energy, E_(elas) is the elasticenergy and E_(elec) is the electrostatic energy for the device. Thefirst two terms in (1), which define the static potential, can beevaluated to assess the range of parameters that yield bistable devices.FIG. 11 shows plots of energy, E_(T)=E_(vdW)+E_(elas), for a single 20nm device as a function of separation at the junction. The series ofcurves correspond to initial separations of 0.8, 1.0, 1.2, 1.4, 1.6,1.8, 2.0, 2.2, 2.4 nm for carbon nanotubes, with two well-defined minimaobserved for initial separations of 1.0 to 2.0 nm. These minimacorrespond to the crossing nanotubes being separated (2.4 nm) and in vdWcontact (0.8 nm). The vdW interaction between nanotubes can becalculated by pairwise summation of a Lennard-Jones potential that hasbeen shown previously to provide good agreement with experiment forfullerene and nanotube systems. The elastic contribution to the totalenergy can be determined using a beam mechanics model: $\begin{matrix}{E_{elas} = {\frac{6\left( {k^{3}B} \right)^{1/4}}{\sqrt{2}\left\lbrack {3 + {3\beta\quad L} + {3\left( {\beta\quad L} \right)^{2}} + \left( {\beta\quad L} \right)^{3}} \right\rbrack}\left( {\delta\quad z} \right)^{2}}} & (2)\end{matrix}$

where B is the product of the nanotube elastic modulus and geometricmoment of inertia, k is the elastic modulus of the support, L is thelength of the suspended nanotube,${\beta = {\frac{1}{\sqrt{2}}\left( \frac{k}{B} \right)^{1/4}}},$is the displacement of the suspended tube from its unstrained position.These calculations show that the proposed SWNT device structure exhibitsbistablility for a broad range of parameters (FIG. 11). For example, a20 nm device in FIG. 11 exhibits room temperature stable (i.e.,barrier>>10 k_(B)T) on and off states for initial separations rangingfrom 1.0 to 2.2 nm. The calculated structures of the SWNT device elementin the off state and on state for an initial separation of 2 nm (FIG.12) highlight the relatively minor distortion of the upper SWNT in theon state, even when the initial separation is near the upper limit forbistability. Si support structures (elastic modulus of 16 GPa) are notshown for clarity. These calculations also show that the potential isbistable for a wide range of device sizes when the upper nanotube issupported on either hard materials, such as silicon (FIG. 13) or softorganic (FIG. 14) materials. FIG. 14 shows calculations on an organiclayer having an elastic modulus of 12 GPa. In FIGS. 13 and 14, the rangeof initial separations yielding bistable devices is shown in gray.Importantly, soft supports enable bistability for smaller devices. Bothtypes of materials can be used for device fabrication. In general, thebistable region increases with device size, and the softer organicsupport yields a larger range of bistability especially in the smalleststructures. The calculations were 15 carried out for (10,10) SWNTs withan elastic modulus of 1 TPa, and Lennard-Jones parameters ofC₆=32.00×10⁻⁶⁰ erg cm⁶ and C₁₂=55.77×10⁻¹⁰⁵ erg cm¹².

There are several important points that can be drawn from thesecalculations. Foremost, is the wide range of parameters that yield abistable potential for the device configuration. The robustness of theon/off states suggests strongly that this architecture will be tolerantof variations in structure that inevitably arise during fabrication by,for example, self assembly. Second, the differences in separationbetween nanotubes in the on and off states will produce largedifferences in resistance (i.e., I˜exp(−kd), where I is the current, kis a decay constant of order 2 Å⁻¹ and d is the tube-tube separation inangstroms), and thus should enable reliable reading of the on/off statesindependent of variations in cross contact resistance. Third, the rangeof mechanical strains required to achieve bistability in FIG. 11,0.22-1.7%, is well below the elastic limit of at least 6% determinedcomputationally and experimentally for SWNTs, and the average bendingangle in the on state is ca. ½ that required to buckle nanotubes. Hence,these device elements can be robust as required for a reliable molecularscale computer. Comparison of the calculated strain energies to valuesof the nanotube-surface interaction and friction suggests that (i) thelower nanotube remains fixed on the substrate, and (ii) the suspendednanotubes do not lift off or slip on supports on the order of 10 nm whenthe suspended tube is deflected to the on state. The interaction withthe support could also be enhanced through chemical modification.

EXAMPLE 2

The effectiveness of switching the suspended nanotube devices between onand off states has been assessed by evaluating the voltage-dependentcontribution of the electrostatic energy to the total energy. In thiscalculation, the boundary element method was used to numerically solvethe Laplace equation for the complex three-dimensional geometry of thecrossed nanotube device. Calculations of E_(T) for switching a 20 nmdevice on and off (FIG. 15) demonstrate that it is possible to changereversibly between the on/off states using moderate voltages, which donot exceed the threshold field for nanotube failure. The switchingvoltages vary depending on the specific device geometry (i.e., shape ofthe static potential), and thus can be further optimized. For example,by using a thinner dielectric layer (that is, 4 vs 20 nm SiO₂) the onand off switching thresholds can be reduced from 4.5 and 20 V to 3 and 5V, respectively. The calculations also show that the electrostaticforces between adjacent nanotubes are insufficient to distort an arrayof elements, even at a 10 nm device scale, because most of theelectrostatic interaction is localized in the small crossing region ofthe individual elements.

This example provides a demonstration of electrostatic switching of thenanotube device. FIG. 15 shows plots of the energy,E_(T)=E_(vdW)+E_(elas)+E_(electro), as a function of separation at thejunction for switching on (FIG. 15A) and switching off (FIG. 15B). InFIG. 15A, the plots (i), (ii) and (iii) correspond to E_(T) for V₁=V₂=0V, V₁=+3; V₂=−3 V and V₁=+4.5; V₂=−4.5 V, respectively, where V₁ and V₂are the potentials applied to the two crossing nanotubes. In FIG. 15B,(i), (ii) and (iii) correspond to V₁=V₂=0 V, V₁=V₂=+15 V and V₁=V₂=+20V, respectively. These potentials are applied with respect to theconducting ground plane (e.g., FIG. 1A). The minimum magnitudes of thevoltages required for switching on and off are 4.5 V and 20 V,respectively. The electrostatic energy was calculated by numericallysolving the Laplace equation using the boundary element method with 3600elements for a 20 nm device supported on Si with a 1.4 nm initialseparation. The calculated electrostatic potential satisfied theboundary conditions and asymptotic behavior.

EXAMPLE 3

Administration of reversible switching and the ability of the device tofunction as a non-volatile RAM is provided in this Example. Propertiesof suspended, crossed nanotube devices made from SWNT ropes were studiedby mechanical manipulation (FIG. 16). Current-voltage (I-V) measurementsmade on the lower and upper nanotubes of a typical model device showohmic behavior with resistances of 11 and 58 kΩ, respectively (FIG.16A). The I-V curves between the upper and lower ropes in the off statewere nonlinear, which is consistent with tunneling, with a resistance onthe order of a GΩ. After switching on, the I-V curves exhibited ohmicbehavior with a resistance of 112 kΩ (FIG. 16B). This large change inresistance is consistent with our predictions for off vs. on states inthe suspended device architecture. Reversible switching betweenwell-defined on/off states has also been observed in devices (FIG. 17).The smaller change in on/off resistances for the device in FIG. 17 isbelieved to arise from large contact resistances that are sometimesobserved with nanotube ropes. Nevertheless, this change between on/offstates is 10-fold, and was persistent. Lastly, it has been found thatsome of the devices fabricated from ropes could only be switched on forreasonable applied voltages. This behavior is expected for potentialsthat have deep vdW minima (e.g., FIG. 11). Irreversible switching can beexploited to configure logic elements for computing.

Those skilled in the art would readily appreciate that all parameterslisted herein are meant to be exemplary and that actual parameters willdepend upon the specific application for which the methods and apparatusof the present invention are used. It is, therefore, to be understoodthat the foregoing embodiments are presented by way of example only andthat, within the scope of the appended claims and equivalents thereto,the invention may be practiced otherwise than as specifically described.

1-89. (canceled)
 90. An article, comprising: an array of memory definedat least in part by an array of nanoscopic wires reversibly moveablebetween a first stable state and a second stable state, the wirespositioned across a series of trenches.
 91. The article of claim 90,wherein the memory is RAM. 92-93. (canceled)
 94. An article, comprising:a memory element comprising a plurality of nanoscopic wires crossing aplurality of conductors, the memory element able to rectify signalsbetween the plurality of nanoscopic wires.
 95. An article, comprising:an array comprising a wire disposed proximate a conductor, the wire andthe conductor together defining a memory element able to be switchedbetween at least two readable states, the array free of means addressingthe memory element to effect switching of the memory element between theat least two states.
 96. An article comprising: an array comprising awire disposed proximate a conductor, the wire and the conductor togetherdefining a memory element able to be switched between at least tworeadable states, the array free of auxiliary circuitry defining thememory element.